Consider the line 9x - 7y = -3.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

The polynomial that represents the area of the shaded region is given as follows:

x² - 3x + 36.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

For the entire region, the area is given as follows:

A = (x + 1)(x + 1)

A = x² + 2x + 1.

The area of the white region is given as follows:

Aw = 5(x - 7)

Aw = 5x - 35.

Then the area of the shaded region is given as follows:

As = A - Aw

A = x² + 2x + 1 - (5x - 35)

A = x² + 2x + 1 - 5x + 35

A = x² - 3x + 36.

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Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

1) The net area between the two functions is 2.

2) The net area between the two functions is 4/3.

3) The net area between the two functions is 17/6.

4) The net area between the two functions is approximately 1.218.

5) The net area between the two functions is 1/2.

The area between the two curves is determined by definite integrals for a interval between two values of x. A general formula for the definite integral is presented below:

\(A = \int\limits^{b}_{a} {[f(x) - g(x)]} \, dx\)   (1)

Where:

Now we proceed to solve each integral:

The lower and upper limits between the two functions are 0 and 1, respectively. The definite integral is described below:

\(A = \int\limits^1_0 {x^{0.5}} \, dx - \int\limits^1_0 {x^{2}} \, dx\)

\(A = 2\cdot (1^{1.5}-0^{1.5})-\frac{1}{3}\cdot (1^{3}-0^{3})\)

\(A = 2\)

The net area between the two functions is 2. \(\blacksquare\)

The lower and upper limits between the two functions are -3 and -1, respectively. The definite integral is described below:

\(A = - 4 \int\limits^{-1}_{-3} {x} \, dx - \int\limits^{-1}_{-3} {x^{2}} \, dx - 3 \int\limits^{-1}_{-3}\, dx\)

\(A = -2\cdot [(-1)^{2}-(-3)^{2}]-\frac{1}{3}\cdot [(-1)^{3}-(-3)^{3}] -3\cdot [(-1)-(-3)]\)

\(A = \frac{4}{3}\)

The net area between the two functions is 4/3. \(\blacksquare\)

The definite integral is described below:

\(A = \int\limits^{1}_{0} {x^{2}} \, dx + 2\int\limits^{1}_{0}\, dx + \int\limits^{1}_{0} {x} \, dx\)

\(A = \frac{1}{3}\cdot (1^{3}-0^{3}) + 2\cdot (1-0) +\frac{1}{2}\cdot (1^{2}-0^{2})\)

\(A = \frac{17}{6}\)

The net area between the two functions is 17/6. \(\blacksquare\)

The definite integral is described below:

\(A = \int\limits^{0}_{-1} {e^{-x}} \, dx+ \int\limits^{0}_{-1} {x} \, dx\)

\(A = -(e^{0}-e^{1}) + \frac{1}{2}\cdot [0^{2}-(-1)^{2}]\)

\(A \approx 1.218\)

The net area between the two functions is approximately 1.218. \(\blacksquare\)

This case requires a combination of definite integrals, as f(x) may be higher that g(x) in some subintervals. The combination of definite integrals is:

\(A = \int\limits^{\frac{\pi}{3} }_0 {\sin 2x} \, dx - \int\limits^{\frac{\pi}{3} }_{0} {\sin x} \, dx + \int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin x} \, dx -\int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin 2x} \, dx\)

\(A = -\frac{1}{2}\cdot (\cos \frac{2\pi}{3}-\cos 0)+(\cos \frac{\pi}{3}-\cos 0 ) -(\cos \frac{\pi}{2}-\cos \frac{\pi}{3} )+\frac{1}{2}\cdot (\cos \pi-\cos \frac{2\pi}{3} )\)

\(A = \frac{1}{2}\)

The net area between the two functions is 1/2. \(\blacksquare\)

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Answer:

√(205)/13

Step-by-step explanation:

The roots of the given quadratic equation are 5 and -4

Quadratics are the polynomial equation which has the highest degree of 2. Also, called quadratic equations.

Given is an equation 3x²-13x-10 = 0, we need to solve by using completing the square method,

The given equation is =

3x²-13x-10 = 0

3(x²-13x/3-10/3) = 0

3(x²-2x·13x/6-10/3) = 0

Adding and subtracting (13/6)²

3(x²-2x·13x/6+(13/6)²-(13/6)²-10/3) = 0

3[(x-13/6)²-169/36-10/3] = 0

3[(x-13/6)²-289/36] = 0

(x-13/6)²-289/36 = 0

(x-13/6)² = 289/36

Taking roots,

x-13/6 = ±17/6

x = 17/6+13/6

x = 5

Or,

x = -17/6+13/6

x = -4

Hence, the roots of the given quadratic equation are 5 and -4

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Answer: C=2πr

r Radius

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

y = -2x + 4  

Step-by-step explanation:

We are given that a line has a slope (m) of -2 and passes through (5, -6).

We want to write the equation of the line.

There are three ways to write the equation of the line:

Any of these forms will work, however let's put it into slope-intercept form as that is the most common way.

As we are already given the slope, we can immediately plug that into the equation.

Substitute m with -2.

y = -2x + b

Now, we need to solve for b.

As the equation passes through (5, -6), we can use its values to help solve for b.

Substitute 5 as x and -6 as y.

-6 = -2(5) + b

Multiply.

-6 = -10 + b

Add 10 to both sides.

4 = b

Substitute 4 as b.

y = -2x + 4  

Answer: y= 5x + 3

Step-by-step explanation:

Lol literally so easy when you understand it so:

the formula for slope intercept form is:

y= mx + b

in this case just plug in the values

hope this helps ;)

also can I get brainliest pls?

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

The bottom table.

Step-by-step explanation:

It's the only one that shows options for heads and tails for every number.

Answer:

D the last one

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

The coordinates of P when written as a fraction and as a decimal, is:

Point P has the coordinates of ( 3/4 , 5/6 ) which means that it is already in fraction form as it has both a numerator and a denominator for the x and ya values.

We can then convert these fractions to decimal form as shown :

x - value : 3 ÷ 4 = 0.75

y - value : 5 ÷ 6 = 0.83

In decimals, it is:

(0.75, 0.83)

In conclusion, as a fraction, point P is ( 3 / 4, 5 / 6 ), and as a decimal, point P is ( 0.75, 0.83 ).

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Hey there! I'm happy to help!

Let's call the hamburgers h and the cheeseburgers c.

h+c=810

c=h+60

Let's plug this value of c into the first equation to solve for h.

h+h+60=810

2h+60=810

Subtract 60 from both sides.

2h=750

Divide both sides by 2.

h=375

Therefore, 375 hamburgers were sold on Wednesday.

Have a wonderful day! :D

Answer:

B

Step-by-step explanation:

Standard deviation is the average distance away from the mean, thus B is correct

Answer:

7606.62

Step-by-step explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

\(p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\\)

Now just equate this to a time 0 payment at the same rate

\(10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62\)

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.

Answer:

Step-by-step explanation:

Therefore, the height of the tower is approximately 121.4 meters.

Answer:

$80 simple interest.

Step-by-step explanation:

That is correct because the simple interest that Sami earns is 4% each year and 4% of %500 is $20. So if she will earn $20 in simple interest a year then in four years she will have earned $80.

I hope this helps!!!! Please mark my answer as the Brainiest!!!!

Thank you so much if you do!!!!

Answer:

Step-by-step explanation:

The expression for the total amount of sales the store makes will be:25s + 28.8p

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the shoe store stocks x pair of sneakers and y pairs of sandals. During a promotion, a pair of sneakers is priced at $50 and a pair of sandals at $36. The shop manages to sell half the sneakers and 80% of the sandal.

Let sneakers = s

Let sandals = p

An expression for the total amount of sales the store makes will be: 1/2(50s) + 0.8(36p).

= 25s + 28.8p

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Answer:

486 if its multiplication

Step-by-step explanation:

18*27=486

Answer:

4 1/2

Step-by-step explanation:

1 1

3

+

3 1

6

=  (1 + 3) + (

1

3

+

1

6

)

=  4 +

1 × 2

3 × 2

+

1

6

=  4 +

2

6

+

1

6

=  4 +

2 + 1

6

=  4 +

3

6

=  4 +

3 ÷ 3

6 ÷ 3

=  4 +

1

2

=  

4 1

2

The correct option for the approximate value of \(\sf -12 + \sqrt{32}\)  is -6.3 to the nearest tenth.

An approximation is anything that is similar, but not exactly equal, to something else.

The given expression is:

\(\sf -12 + \sqrt{32}\)

The value of \(\sqrt{32}\) is given as 5.656

Since, after decimal 6 to the right of 5 is greater than 5

To the nearest tenth, we can write as 5.66

\(\sf \therefore \sqrt{32} = 5.66\)

For the required value of the expression we can write,

\(\sf -12 + \sqrt{32}\)

Put the value of \(\sf \sqrt{32} = 5.66\)

Putting values in expression we have,

\(\sf -12 + \sqrt{32} = -12 + 5.66\)

Solving them

\(\sf \rightarrow -12 + \sqrt{32} = -6.34\)

Hence, the approximate value of \(\sf -12 + \sqrt{32}\) is -6.3 to the nearest tenth.

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